{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "569d620b-882a-4d90-a82a-e0c2bb85de9d",
   "metadata": {},
   "source": [
    "\n",
    "姚端正、周国全、贾俊基《数学物理方法》第四版P.275\n",
    "\n",
    "里兹法重解例题3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e9220533-845d-4da3-88cf-4e204859b2e2",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *  # 导入sympy 包中所有的函数\n",
    "from sympy.abc import x # 引入默认的符号变量\n",
    "c0,c1,c2,lamd = symbols('c0 c1 c2 lambda') # 自定义符号变量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b1db7b4c-a630-474c-8c8a-0e2f2e33cc43",
   "metadata": {},
   "outputs": [],
   "source": [
    "ux = x*(x-1)*(c0+c1*x+c2*x**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "81a5c4fa-ff42-41c2-ba96-ca44ec677482",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}^{2}}{3} + \\frac{c_{0} c_{1}}{3} + \\frac{c_{0} c_{2}}{5} + \\frac{2 c_{1}^{2}}{15} + \\frac{c_{1} c_{2}}{5} + \\frac{3 c_{2}^{2}}{35} - \\lambda \\left(\\frac{c_{0}^{2}}{30} + \\frac{c_{0} c_{1}}{30} + \\frac{2 c_{0} c_{2}}{105} + \\frac{c_{1}^{2}}{105} + \\frac{c_{1} c_{2}}{84} + \\frac{c_{2}^{2}}{252}\\right)$"
      ],
      "text/plain": [
       "c0**2/3 + c0*c1/3 + c0*c2/5 + 2*c1**2/15 + c1*c2/5 + 3*c2**2/35 - lambda*(c0**2/30 + c0*c1/30 + 2*c0*c2/105 + c1**2/105 + c1*c2/84 + c2**2/252)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "J  = integrate(diff(ux,x)**2,(x, 0, 1)) - lamd* integrate(ux**2,(x, 0, 1))\n",
    "J "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "25edbd4e-f5cc-4198-9adc-727b92971e53",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 c_{0}}{3} + \\frac{c_{1}}{3} + \\frac{c_{2}}{5} - \\lambda \\left(\\frac{c_{0}}{15} + \\frac{c_{1}}{30} + \\frac{2 c_{2}}{105}\\right)$"
      ],
      "text/plain": [
       "2*c0/3 + c1/3 + c2/5 - lambda*(c0/15 + c1/30 + 2*c2/105)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq0= diff(J,c0)\n",
    "eq0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "69f46e53-7489-42ea-988c-46b5bed6d127",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}}{3} + \\frac{4 c_{1}}{15} + \\frac{c_{2}}{5} - \\lambda \\left(\\frac{c_{0}}{30} + \\frac{2 c_{1}}{105} + \\frac{c_{2}}{84}\\right)$"
      ],
      "text/plain": [
       "c0/3 + 4*c1/15 + c2/5 - lambda*(c0/30 + 2*c1/105 + c2/84)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq1= diff(J,c1)\n",
    "eq1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f61235f5-dcbc-4e77-a3d9-80665c175883",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{c_{0}}{5} + \\frac{c_{1}}{5} + \\frac{6 c_{2}}{35} - \\lambda \\left(\\frac{2 c_{0}}{105} + \\frac{c_{1}}{84} + \\frac{c_{2}}{126}\\right)$"
      ],
      "text/plain": [
       "c0/5 + c1/5 + 6*c2/35 - lambda*(2*c0/105 + c1/84 + c2/126)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eq2= diff(J,c2)\n",
    "eq2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "19071805-db55-4ac0-b6d1-99449c30a5e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0\\\\0 & 0 & 0\\\\0 & 0 & 0\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[0, 0, 0],\n",
       "[0, 0, 0],\n",
       "[0, 0, 0]])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c=zeros(3)\n",
    "matrix_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "de5a1f7c-c568-49d8-9a61-42411ed5c9dd",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = [c0,c1,c2]\n",
    "eqs = [eq0,eq1,eq2]\n",
    "for i in [0,1,2]:\n",
    "    for j in [0,1,2]:\n",
    "        matrix_c[i,j]= expand(eqs[i]).coeff(c[j])\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "26353137-749f-4f00-8fbc-7df8633c1c72",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\frac{2}{3} - \\frac{\\lambda}{15} & \\frac{1}{3} - \\frac{\\lambda}{30} & \\frac{1}{5} - \\frac{2 \\lambda}{105}\\\\\\frac{1}{3} - \\frac{\\lambda}{30} & \\frac{4}{15} - \\frac{2 \\lambda}{105} & \\frac{1}{5} - \\frac{\\lambda}{84}\\\\\\frac{1}{5} - \\frac{2 \\lambda}{105} & \\frac{1}{5} - \\frac{\\lambda}{84} & \\frac{6}{35} - \\frac{\\lambda}{126}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[   2/3 - lambda/15,     1/3 - lambda/30, 1/5 - 2*lambda/105],\n",
       "[   1/3 - lambda/30, 4/15 - 2*lambda/105,    1/5 - lambda/84],\n",
       "[1/5 - 2*lambda/105,     1/5 - lambda/84,  6/35 - lambda/126]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "41ea76a9-df1f-4662-b538-903745ae24d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - \\frac{\\lambda^{3}}{55566000} + \\frac{11 \\lambda^{2}}{3969000} - \\frac{17 \\lambda}{165375} + \\frac{2}{2625}$"
      ],
      "text/plain": [
       "-lambda**3/55566000 + 11*lambda**2/3969000 - 17*lambda/165375 + 2/2625"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_c.det()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "4b7aea0c-06b2-4aec-a70b-83b5fa415006",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[56 - 4*sqrt(133), 42, 4*sqrt(133) + 56]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd = solve(matrix_c.det(),lamd)\n",
    "sol_lamd.sort() # 排序\n",
    "sol_lamd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1aed06f5-f346-4638-8e63-34717f301f01",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 4 \\sqrt{133} + 56$"
      ],
      "text/plain": [
       "4*sqrt(133) + 56"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sol_lamd[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2805e586-4b89-4da4-8641-9284c575db05",
   "metadata": {},
   "outputs": [],
   "source": [
    "condition = integrate(ux*ux,(x, 0, 1)) -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "f5f452d0-820a-46ce-927b-22cb3c1e44eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(10)*sqrt(266 - 23*sqrt(133)) - sqrt(1330)*sqrt(266 - 23*sqrt(133))/19,\n",
       "  -3*sqrt(353780 - 30590*sqrt(133))/19,\n",
       "  sqrt(8820 - 14490*sqrt(133)/19)),\n",
       " (sqrt(1330)*sqrt(266 - 23*sqrt(133))/19 + sqrt(10)*sqrt(266 - 23*sqrt(133)),\n",
       "  3*sqrt(353780 - 30590*sqrt(133))/19,\n",
       "  -sqrt(8820 - 14490*sqrt(133)/19))]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_1=[eq0.subs(lamd,sol_lamd[0]), eq1.subs(lamd,sol_lamd[0]),\n",
    "       eq2.subs(lamd,sol_lamd[0]),condition]\n",
    "c_sols_1 = solve(eqs_1, c0,c1,c2)\n",
    "c_sols_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "217615b0-b8c5-4d71-8649-cf10c54fa08a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(210), 2*sqrt(210), 0), (sqrt(210), -2*sqrt(210), 0)]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_2=[eq0.subs(lamd,sol_lamd[1]), eq1.subs(lamd,sol_lamd[1]),\n",
    "       eq2.subs(lamd,sol_lamd[1]),condition]\n",
    "c_sols_2 = solve(eqs_2, c0,c1,c2)\n",
    "c_sols_2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "be5f236f-e65e-4833-ab5f-0b78eb28eb7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(-sqrt(10)*sqrt(23*sqrt(133) + 266) + sqrt(1330)*sqrt(23*sqrt(133) + 266)/19,\n",
       "  3*sqrt(30590*sqrt(133) + 353780)/19,\n",
       "  -sqrt(14490*sqrt(133)/19 + 8820)),\n",
       " (-sqrt(1330)*sqrt(23*sqrt(133) + 266)/19 + sqrt(10)*sqrt(23*sqrt(133) + 266),\n",
       "  -3*sqrt(30590*sqrt(133) + 353780)/19,\n",
       "  sqrt(14490*sqrt(133)/19 + 8820))]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 求 c0,c1 \n",
    "eqs_3=[eq0.subs(lamd,sol_lamd[2]), eq1.subs(lamd,sol_lamd[2]),\n",
    "       eq2.subs(lamd,sol_lamd[2]),condition]\n",
    "c_sols_3 = solve(eqs_3, c0,c1,c2)\n",
    "c_sols_3 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6ef2fbce-3548-4085-897c-716e5217dd7b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x21b15874b50>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ux_1=ux.subs([(c0,c_sols_1 [0][0]), (c1,c_sols_1 [0][1]),(c2,c_sols_1 [0][2])])# 基态试探解\n",
    "ux_ex_1= sqrt(2) *sin(pi* x) # 基态精确解\n",
    "plot(ux_1,ux_ex_1,(x,0,1)) # ,legend=True\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "21b0d17d-aef0-4327-b326-c47f59d3bc22",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x21b26e13d50>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ux_2 = ux.subs([(c0,c_sols_2 [0][0]), (c1,c_sols_2 [0][1]), (c2,c_sols_2 [0][2])])# 第一激发态试探解\n",
    "ux_ex_2 = sqrt(2) *sin(2*pi* x) # 第一激发态精确解\n",
    "plot(ux_2,ux_ex_2,(x,0,1)) # ,legend=True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "13120c2f-2c4c-4c9f-a458-092f4e64d535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x21b26eb8910>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ux_3 = ux.subs([(c0,c_sols_3 [0][0]), (c1,c_sols_3 [0][1]), (c2,c_sols_3 [0][2])]) # 第二激发态试探解\n",
    "ux_ex_3 = sqrt(2) *sin(3*pi* x) # 第二激发态精确解\n",
    "plot(ux_3, ux_ex_3, (x,0,1)) # ,legend=Truev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "c5ed5b50-676c-4946-ad6c-5c4e0d3bf841",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 102.130250378683$"
      ],
      "text/plain": [
       "102.130250378683"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(sol_lamd[2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "fcfa79e3-0169-4bee-96ff-45ad12375e64",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -28.6462005494646$"
      ],
      "text/plain": [
       "-28.6462005494646"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N(c_sols_3[0][0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "3d26fe62-b3c5-4d18-af81-3d127fc58f6e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle -13.3037104471$"
      ],
      "text/plain": [
       "-13.3037104471000"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N((3*3.14159)**2)-102.13\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "e8ee0ab3-e904-4325-87bf-0ec5efbe66c2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dihUrcOnSJWzevJl1FCIDW7ZsQdu2bbF3717069ePdRzZk02vNwmeiooKrF27Fq+//jpatGjBOg6RgdatW2PNmjV48803UVFRwTqO7FGhjAILFy6EQqHA3//+d9ZRiIxMnjwZR44cgcFgYB1F9qhQRrgLFy5g3rx5+Otf/0qDjImbBg0aID09HcuXL8fVq1dZx5E1KpQRLjk5GR06dKAOLeLRjBkz8OCDD2L8+PGso8gaFcoIdvr0aezdu5c6cEiNNm7ciIMHD9Y4d0K0o+FBEWzGjBlo1qwZFi9ezDoKkbmpU6fiwoULNHTMi4gtlNE+4Hzr1q14/vnnUVpaipYtW7KOQ2Tu1KlT6NKlC2w2GwYOHMg6juzQpXeESklJwTPPPENFkvikY8eOGDZsGCZPnsw6iixRoYxAWVlZcDgceO+991hHIWFkw4YNuHTpEvbs2cM6iuxQoYwwoijivffeg8FgwL333ss6DgkjCoUC7777LhYsWIAIvSNXZ1QoI8zq1avRsGFDpKWlsY5CwtBf/vIXfPvtt1i0aBHrKLISsYXStRTEpk2bWEcJmdu3b2PWrFmYNGkSrc9N6qRhw4Z49dVXMX/+fNy5c4d1HNmgXu8IMmnSJOzYsQOXL19mHYWEsYqKCrRq1QqTJk3CypUrWceRBWp2RIhbt25h06ZN9IdN6q1BgwZYsWIFvvjiC2pV/n9UKCPEe++9hxEjRuC5555jHYVEgMmTJ6NNmzZ4/fXXWUeRBSqUEeCnn36CwWDAggULWEchEWTGjBl455134HA4WEdhjgplBJg4cSLatm2L7t27s45CIkhycjIefvhhWl8JETzDebSw2+3417/+hW+++YZ1FBKBcnJyMGrUKNy4cQPNmzdnHYeZiG1RRsvwoMzMTPTt2xePP/446ygkAg0dOhTJyclYvXo16yhM1Tg86MyZM7BYLMjPz3e7T6FUKjFkyBDodDr8/ve/r/UggiDAarWC4zgIggC9Xu91TW6r1QqtVgsA1bbheR4AoFKpIAgCnE4nVCqVx/1Ew/AgQRDQp08fFBcX06qKJGi+//57PPbYYygpKUH79u1Zx2FD9MJoNIpz5swReZ73+DzP89I2tVGpVNLndrtd1Ol0XrcFUO3DZDKJoiiKer1eekyr1YoOh8PrfkaNGlVrrnCnVqvFPn36sI5BokC3bt3E/v37s47BjMdCmZmZKTqdTp924HQ6ayyWdrvdrVCKoigqFAqP2zocDtFisbg95iqSoiiKZrNZdDgcNRZIl0gvlEVFRWJMTIx48uRJ1lFIFDhw4IAYExMjlpSUsI7ChMd7lLNnz/Z5eq6WLVsiIyPD6/M2mw1KpdLtMaVSKV1GV6XT6aTPrVar29fAb5fj3i7bo8kLL7yAxx9/HF27dmUdhUSB3r17Y9CgQVixYgXrKEz41Jlz7do1nDlzpk4H8Da9fFlZWbXHKhdAp9OJsrIycBzn9pjVaoXVaoXRaIQgCHXKFO5KS0tx/vx5fPjhh6yjkCjywQcfYOPGjTh16hTrKCHn0/CghQsXYsuWLSgpKcHVq1dhsVgwbdq0eh24tvU5jEYjTCaT22OVO4E4jsOQIUNgt9s9fr+r19slkpaEmDhxIp577jkkJCSwjkKiSJs2bdC2bVtMnDgR3377Les4oeXL9bnVaq32WE5Ojk/X9maz2eM9yvz8fK/f43A4RI7jqj1eVFTktg0A0W63e9xHpN6jdN0r8nbehATT4cOHo/LeuE+X3iqVComJiViyZIl0CS76OOmQa6hPVRqNxuv3HDp0yOPQoMGDB1fbtur9z0g3depU9OvXz+2WBCGh0qNHD/Ts2bPeV5ThxqdCmZ2djUWLFkEUReh0OsTFxfl82Vf1BS0IAjQajVQIeZ6vdq+R5/lqBZDjOLdLcZvNBp1OF1UdO+fOncMPP/yADz74gHUUEsU2b96MH3/8EVeuXGEdJWR8ukfJcRwGDx6MwYMHY/bs2SguLsbp06d9PojFYoHRaERiYiIKCwthsVik5zIyMpCYmAiDwVDtmJUpFApoNBpkZmZCoVDAbre77ScaLF26FK+99hq1JglTnTt3xuDBgzFhwgTs2LGDdZyQ8Gni3tOnT2Pnzp0YO3Ys7rvvPqSmpiIhIUHWze9Ie2dOcXExevfujfPnz+N3v/sd6zgkyvE8D41Ggx9//BEdO3ZkHSfofLr07tChA6ZNm4b77rsPwG+tPWrVhNbUqVOh0WioSBJZUKlU6N69O6ZMmcI6SkhUa1FevXoVDofDp/dwu1y7dg0ApEIqB2q1GvHx8RExLOi7777DY489huPHj6Nbt26s4xACADh48CAGDBiACxcuRPz68dValC1btkR+fj4++eQTn3awZcsW5OXlyapIAkB8fDy2bdsW9kUSANasWYMRI0ZQkSSy0rt3b0yaNAnLli1jHSXovN6jLC4uRkZGBhISEpCYmAiO46BQKOB0OiEIAg4ePIjTp08jJSUFgwYNCnXuWkXKPcpTp06hd+/eOH78OB566CHWcQhxc/ToUfTq1Qv//ve/8fDDD7OOEzS1duZcvXoVeXl5sNvtcDqdUCgUSEhIgFarRYcOHUKV02+RUij79+8Pp9OJo0ePso5CiEedOnVC586dsX37dtZRgqbW4UEtW7bE9OnTQ5GFVHHu3Dns3bsX+/btYx2FEK9WrlyJkSNH4sqVK4iLi2MdJyh86vWeM2cOUlNTsWvXrmDnIZXMmDEDnTt3Rp8+fVhHIcSrYcOG4YknnsD69etZRwkan8ZRui6/8/PzYbPZkJiY6NcM5yyEe6/3zZs30bFjR3zxxRfo1asX6ziE1Ojo0aPQarWw2+1o0aIF6zgB51OhrIrnecyZMwcAkJCQgDVr1gQ8WH2F+z3KiRMn4qeffsLOnTtZRyHEJw8++CCGDx+O999/n3WUgPN5PsrKl90qlQopKSn45z//Cb1ejyVLlgQtYDS6ceMGNm3ahJdffpl1FEJ8lp6ejg0bNqC8vJx1lIDzqVAaDAasXbsWnTp1wksvvYR169bBZrMBAHr16iXr3u9wNHPmTLRu3RrPPvss6yiE+GzatGlo1qwZ0tPTWUcJOJ8KpVqtRl5eHkpKSqDVauFwOGAwGHD16lVoNBrExMQEO2fUuHv3LrZt24b58+ezjkKI3z766CNs27bN52kYw4XP9yg/+eQTjy2c4uJiWXY2hOs9yg0bNuAf//gH3ZskYUkURWluiLlz57KOEzA+tSgBeL0MlGORDFcVFRXQ6/VITk5mHYWQOomJiUFycjIWL17MOkpA+Vwow41rzZxNmzaxjuKzRYsWAYCsp68jpDYLFizA7du3sXbtWtZRAqZOw4PCQTheerdq1QpTpkzB0qVLWUchpF5mzJiBgwcP4tChQ6yjBETEtijDzb59+9CkSZMa10gnJFxkZWXh8uXLOHDgAOsoAUGFUiYMBgPefvttNGrUiHUUQuqtUaNGeOKJJ8LyXXGeUKGUge3bt+Pbb7+lThwSUZYtW4azZ8/im2++YR2l3qhQysCsWbMwdOjQiJ8lmkSXBx54AH379sXMmTNZR6m3iC2U4dLrfeLECZSUlMjy/fKE1JfZbMaZM2fCfmlb6vVmbPbs2fj111+RlZXFOgohQTFt2jRUVFTgH//4B+sodRaSQikIAqxWKziOgyAI0Ov1UCgUHrfleR7AbxNvCIIAp9MJlUrl937CoVCeO3cOXbt2xalTpyJ6Gn0S3Xbu3Ik//elPuHz5MpRKJes4dSOGgEqlkj632+2iTqfzuq1erxcBiABErVYrOhyOOu1n1KhR9QsdAiNGjBA7duzIOgYhQdemTRvxueeeYx2jzmpdCqK+BEFw+5rjOGnmIU/UajUcDgcAuLUW/d2P3N24cQNfffWVz6tdEhLO0tPTkZKSgrt37yI2NpZ1HL8FvTPHZrNVa24rlUrpEtsThUJR7ZK6LvuRsxUrVqBNmzZ4+umnWUchJOgmT56MPn36hG3DIOiF0ul0eny8rKzM6/ZWqxVWqxVGo1FqSfq7Hzm7e/cuPv74Y3z88cesoxASMi+++CJmzpwZllOwBf3S2xtvha9yBw3HcRgyZAjsdrvf+3END3KR09o5CxYswMWLF/HEE0+wjkJIyCQlJeEvf/kLVq9eHXaz9we9UCoUimqtvrKyMq+91YIgSL3crt5tQRD83k98fLxse72XLVuGKVOm0ITHJKrExsZi/PjxmD9/ftgVyqBfemu1Wo+PazSaao/xPI/BgwdXe1ypVPq1HznbsGEDbty4gYULF7KOQkjIZWVl4dq1azhy5AjrKH4JeqHkOM7ta0EQoNFopJYgz/PSfUiO42AymaRtbTYbdDodFApFrfsJF5s2bUJKSgoaN27MOgohIdeiRQu8/fbbWL58OesofgnZgHOz2YzExEQUFhYiNTVVKnBJSUlITEyEwWAA8FvhtNlsUCgUsNvtboWzpv1UJccB50VFRRg2bBjOnj2Le++9l3UcQpi4dOkSHnroIRw7dgyPPPII6zg+obcwhpBGo0GjRo2wb98+1lEIYapHjx5o1aoVdu/ezTqKT2hSjBD597//DZ7nsWrVKtZRCGFu+fLlKCgoCJvJMqhFGSKjR4/G8ePHUVJSwjoKIbLQt29f6HQ6zJo1i3WUWkVsi1JOysvLcejQIbz//vusoxAiG8uXL8eyZctw584d1lFqRYUyBP7+978jPj4e/fr1Yx2FENnQaDS4evUq0tPTWUepFRXKIBNFEStXrqT3dBNSRUxMDPR6fVgMFaJCGWSrV6/GnTt3MGfOHNZRCJGdBQsW4MaNG7Barayj1IgKZZCtWrUKzz//fFhOLUVIsDVu3BhpaWmyL5QR2+utVqsRHx/PdDKMH374AYMHD4YgCLQMLSFe3Lx5Ew8++CB2794NtVrNOo5HEVso5TA8SK1Wo2vXrtiwYQPTHITIXWJiIu655x7ZvhmDLr2D5MyZMyguLkZqairrKITIXlZWFvbv34/Lly+zjuIRFcogmTlzJjp16oTu3buzjkKI7D3xxBPo0KEDFi1axDqKR1Qog6C8vBz79u3D4sWLWUchJGxYLBZs3boVd+/eZR2lGiqUQZCdnY0+ffrQ2ElC/KBSqXD79m2kpaWxjlJNxBZKVpNiiKKI1NRUehcOIXWQnJyMd999l3WMaqjXO8DWrVuHl19+GTdv3kTDhsyWJCIkLN26dQstWrRAXl4enn32WdZxJBHbomQlLS0NY8aMoSJJSB00bdoU48ePl90EMlQoA0gQBNy6dSss3rtKiFy9++67+Pbbb2U1JSEVygCaNWsWJk2ahNatW7OOQkjYatGiBeLj4/Hiiy+yjiKh68MAuXTpErZt24b9+/ezjkJI2Fu8eDGGDx+O69evo0WLFqzjUIsyUF599VW0adMGvXv3Zh2FkLD3pz/9Cffff7+06CBrEVsoQzk86O7du/jss8/w5ptvBv1YhESLZcuW4euvv4YcBuaEbLlaq9UKjuMgCAL0er3XZWZdy9UCQGFhIXJyctzWAAd+G5gqCAKcTidUKpXH/YRyeNBnn32GJUuWYM+ePYiJiQnJMQmJdKIoomvXrjAajZgyZQrzMEGnUqmkz+12u6jT6bxuazKZ3D6v/L16vV4EIAIQtVqt6HA4vO5n1KhR9Qvth3bt2omrVq0K2fEIiRYTJkwQ4+PjWccQg37pLQiC29ccx0ktxqp4nkdGRob0tU6nA8/z0j7UajUcDgccDgfy8/O9tkpD6fPPP8f58+cxefJk1lGY43keRqORdYwaqdVq2U8S6wubzQa1Wo3s7Ox67UfuP4+srCyUlpbim2++YZoj6IXSZrNBqVS6PaZUKqXL6MpUKhVycnKkr51Op7S9i0KhkEWBdDEajRg0aBCaNWvGOgpzZrO53i/cYDOZTNBqtUHbv+tvNti0Wi2Sk5P9/r6q+YL986ivuLg4/PGPf8Qbb7zBNEfQC6W3P5yysjKPj+t0Ounz3NxcaLVaqTA6nU5YrVZYrVYYjcZqrdVQu3z5Mux2O1auXMk0h1woFAo4nU6vVwxyUPnvKdAEQUBeXl5Q9h0InvIF8+cRKJs3b8bx48dx7do1ZhmYjaOs7T+vqygWFRVJj1XuBOI4DkOGDIHdbvf4/a5eb5dgLAmxZs0aTJ06FV26dAnofsORzWZDcnIyeJ6HxWKRdSslWEwmk2yXMgDkn8+bdu3a4ZFHHsErr7yCDz74gEmGoLcoFQpFtdZjWVlZrf/FjEZjtfuQlVuQrh50b63K+Ph4bNu2TfoIdJG8ffs25s+fj6SkpIDuN1zxPA+VSoWUlJRqrRabzYaEhASkpKTAarUiOzsbKSkp0j9LX5/Pzs5Gdna29GLneR6ZmZmwWq3IzMyURleo1WokJCQAADIzM5GQkIDMzEzwPO92X6/yfT6bzYbs7GwkJSVBEARp3ykpKW7nYrVapW0r34+12Ww4dOgQ8vPzkZ2dLf1d2mw2KWNN92+dTqeUo/K2ns7RE9e5ZGZmSjkTEhKk1r2nfFV/HjUdz9vPKlTGjx+PTZs24c6dOyE7pptg9xbZ7Xa3nmtRFEWFQlFjj7XJZBLtdrsoiqLocDhEh8MhFhUViQqFQtrG4XCIALzuJ9i93q+99prYqlWroB4jnFQerQBAzM/Pd3veYDC4bWOxWEStVuvz83q9XtTr9dJzdrvd7XlR/G10hevvxfW52Wx2+xsxmUyi2Wx2O27lURhardYtB8dxbt8PQPrb1Ov1osVicdtX5X1X/ds3m81u+67MZDK5/czMZnON5+jpXEwmk9v+dTqd2z6r5qu6j9qO5+lnVVRU5PF8Aq2iokJs1qyZuHDhwpAcr6qgtyg5jnP7WhAEaDQat7GRlf9LWq1WqFQqcBwHp9OJvLw8KBQKcBwHk8kkbWez2aDT6ZjdX8nJycFLL70U9OOkp6ejSZMm0kdpaSlyc3PdHtuzZw+Ki4vdHlu3bh1u3rzp9pjrXQ4JCQnSY6NHjwYADB8+HE2aNEF6errfGW02G+x2u9Ti4zgOFoul2naVf1c6nQ42m83tFkxNzysUCqmVqNPpYDabq42h5ThO+nvJycmBWq12+1vzJC4uDomJiW4ZKv/NVr0icjgc0tVMWVlZjffJzWYzlEolbDab29hgT3Q6HZKSkqRW4dixY2s8x2Co7Xieflbe+hoCLSYmBtOnT8fHH38ckuNVFZJ7lBaLBUajEYmJiSgsLHR7EWVkZCAxMREGgwGCIFRrzisUCunepEajQWZmJhQKBex2u8cXYyjs378fTZo0wbx584J+rLlz52Lu3LlujyUnJ3vs8bx9+7ZPj3m6r7tjx446Z+R5HmazWfpaqVRi+vTpbo8FQtV/ujVRKBRQqVTIzc31+qaEmr7Xm4yMDMTFxUGn09WYx1XgVSqV2/1avV7vcXulUgmHwwGe55Gbm4ukpCS/c/vD6XTKvhOnqsWLF+PTTz/F4cOH0bNnz5AeOyRvYXS1BnU6HUwmk9svyGKxSC0djuMgiqLbh8PhkLZVqVQwGAzQ6/VurctQmz9/Pt58803cc889zDLImU6n89j7Xbn1aLVaq/W41vZ85dZLcnJytf3zPI+xY8dKx7ZYLNJ9S285PPH2vM1mA8/zMBgM0hWP63FP23rK6G1EQEZGBgRBgEqlkl4jNZ2jp6wKhQJXrlxxO1ZN51J1H74cj6WGDRtCpVIxGbNMswf56cSJE9ixYwdWr17NOgpzNpsNJpMJZWVl0Gq1UgsoOzsbCoUCRqMRKSkpUivKbrdLL96qVxY1Pe+6dOV5HhzHSccymUzIzMwEx3HS9nl5eTCZTFInTGJiIqZPnw5BEKDVapGbmwulUikV89zcXAC/DZNxdXAAv/1TttlsEAQBJpMJJpNJuox3FZOkpCSYzWapZZmSkgKTyYTs7GxotVqpgeC6mnIdx5O4uDhpzHFZWRmSk5O9nqNCoZBanq59qlQqjB07FkajUcqn1Wqly2mO46rlc+3D9fPw53iun5Xr/P1p7ddHWloaHnvsMZw7dw7t2rULyTGBCF4KQq1WIz4+PuDDgrRaLS5evIhjx44FbJ/RwGg0IiEhweulZ23PE+LSsWNHPProo/j0009DdsyIbVG6hgcF0i+//ILdu3fjf//3fwO6X0KI7zIzMzFjxgzcuXMnZEuuROw0a8FgsVgwYMAADB8+nHWUsOK6dLZYLB7fulrb84RU9uyzz6JLly4B7yysScReegd6mjVRFNGuXTusXbsWI0eODNh+CSH+mzVrFtavX+/WeRVM1KL00fr163Hx4kUMHTqUdRRCot6CBQtw9epVfPbZZyE5HhVKH6WlpeGZZ56hZWgJkYGmTZti8ODBeP3110NyvIgtlIFcCuL06dM4d+4csrKy6h+MEBIQZrMZFy5cwM8//xz0Y9E9Sh+88cYbKC8vx+LFiwOyP0JIYCQnJ6NJkyZYv359UI8TsS3KQLl27RqWLl3Kfs0OQkg1Op0OGzduRHl5eVCPQ4WyFkajES1btkS3bt1YR5EdnueRkpKCmJgYGI1GZGdnIzMzE0ajEa1atZL1BL6eRMvyCpEkKSkJzZo1C/68C0zmLAqBQEyzxnpqp3Bgt9s9TndXVFRUbUqvQKppmr76qDp1WV2y5OfnBy0fqe61114TH3744aAeg1qUNdi1axcaN24sm0XY5ajqekguwZz5Rk5LLoTr8gqRZOHChWjSpAmKi4uDdgwqlDVYvXo1Fi1ahNjYWNZRwkbl+UWDNesMy5mjqpJTlmh1zz33YNiwYXjhhReCdoyILZT1HR50+PBhbN26lZZ68JHr/uT06dOlxxQKRY1LMwDel1YAfmutGY1GaXkI1/RpnpZc8ISWV4ge//3f/42jR496XUOr3oJ6Yc9Qfe9R9u/fX+zVq1eA0kSuqktyVF7Go/I23pZmgJelFRwOh9syDJWXivC0pIEntLxCdOnSpYs4YsSIoOyb3mbiwfXr17F3715Z9No2a9YMd+/eDdnxYmNjcfPmzTp/f+Xlhm02m3S/zrU0g2t+QxeHwwGFQlFtaYW8vDxwHCdtm5qaWqcsarUaHMchOTkZer0eGRkZXpc7CMYUbzUtr6DX6xEXF4e4uDjpuVAurxBpFixYgGnTpgVlVqGIvfSuj82bN0Oj0WDgwIGso+DmzZu4fft2yD7qUyQBuE3iWvmStvLSDJVlZGRIl7aVJ3+tulSBQqHw2EFS02zlruUVcnJycOXKlaBf1tY2czoJrjFjxkCj0VT7GwsEKpRViKKIxYsXY+HChayjhAVvrR+n0ymtye5taYaallbQ6XTVplzztuSCN7S8QvR58sknMXPmzIDvly69q1i3bh3Onj2Lp556inUU2au8qFhGRobUYeNakTE1NRXZ2dlel2ZwLRrnaWkFjuNgNps9LqNQdUkDb2h5hehjNBqRlpaGLVu2YMyYMQHbb8S+17uuS0H8/ve/R58+fbB58+YgpiOEBMvIkSNht9vx/fffB2yfEduirMtSEMeOHcO5c+ewf//+IKUihATbihUroFKpcOXKFbeOsvoISaF03ZdyLRzvuuTyd1t/9lMXubm5SElJwYMPPhiwfRJCQishIQFjxozBvHnzsHLlysDsNCiDjqpQqVTS53a73W3cmD/b+rMff8dROp1OsXnz5tXGABJCwo/VahVjY2PF27dvB2R/Qe/1rvquB47jvPZU1rStP/upC6PRiGbNmtENdEIiwJgxY9CiRQu89dZbAdlf0Aulq9exMqVS6XU1Pm/b+rMff1VUVOCjjz7CrFmz6r0vQog8pKSkICcnJyD7Cnqh9DbmzNP4u5q29Wc//vr8888BAK+99lq990UIkYe0tDS0aNECx44dq/e+mPV6+/Muhpq29faca1IMl5qGCfXr1w979+5FgwY0/p6QSNGoUSNs2bIF7dq1q/e+gl4oPb13tayszGNvdU3b+rMfwL/hQUql0uu8ioSQ8KXRaAKyn6A3oby9c8LTCdS0rT/7IYSQQAp6i7JqL7IgCNBoNFJLkOd5KBQKj2/Zqrxt1ZZj1f0QQkiwhOQepcVikd6z63qvq0tGRgYSExOl5RZq2ram5wghJGgCMhpThvwdcL5x48YgJQmtSDgPOgd5iIRzEMXAnEfEdvP6uxREXZeMkJtIOA86B3mIhHMAAnMeEVsoXb3e/swc5C9/fwHB3r4u6ByC9z3B3n80/i5YFe+ILZShEAl/FHQOwfueYO8/Gn8XrAplxM5H+Yc//EGaSNYX58+fR3x8vF/H8Pd7gr29HDNFwjlQpujKFB8fjzVr1rg9FrGFkhBCAoUuvQkhpBZUKAkhpBZUKAkhpBYRu2ZOVYFajoI1f7K55vEEgMLCQuTk5MjiPOr68zUajUhNTQ3Lc7DZbBAEQXqbbk2rR4aSv68L17ywgiBAp9PJYqJrnucxffp0aXlkb+r1uq73kPUwEajlKFjzJ5vJZHL7vPL3slSXn29RUZEIQHQ4HEFM5jt/ziE/P1/U6/XSthzHBT2fr+r69ySKonROLFksFulvozb1eV1HRaG02+3VioRCoaj3tqHmT7aioiK35+x2uwiA+ZpAdf35WiwWkeM4WRRKf8+ham7WvwMXf8+j6rZyKJQutRXK+r6uo+IeZaCWo2DNn2wqlcptGnzXBMes592sy8/XarVCp9MFO5rP/DkHQRCkeVN5nofT6ZTF5Srg/+9CqVRCrVZLl+BDhgwJRcyAqO/rOioKZaCWo2DN32yVi0tubi60Wi3z+3v+noPT6WSeuSp/zoHneSiVSuneWHZ2NqxWa5AT+sbf34Vrtq6EhARYLBZZ/fOqTX1f11HTmeNJoJajYK22bE6nE1artdab3Sx5O4e8vDzo9frQhqkjT+dQVlYGQRCkf1J6vR6tWrWCKOP3eXj7XdhsNphMJgiCgJSUFACA2WwOYbLA8/V1HRUtykAtR8FaXbMZjUbk5+eH3TnYbDaMHTs2RMl85885cBznNvF05QmrWfPnPARBQGFhIbRaLfR6Pex2O/Ly8qotIy1X9X1dR0WhDNRyFKzVJVtmZiaMRiM4joPT6WTeMvb3HPLy8pCdnY3s7GwIgoCMjAzmRcafc5DL/UhP/DkPnueRmJgofc1xHFJTU5n/Pfmqvq/rqCiUvixH4frPWNu2LPlzHsBvnSAqlUoqknl5eczPw59zcLVeXB/Ab2s1q1SqkGauyt+/J41GIxUU11hK1ucA+HceKpUKhYWFbttfuXJFFufhUrVoB/R1XZeu+HBkt9tFg8EgWiwW0WAwuA3X0Ol0bmPEatqWNV/PwzUcqPKHnIY5+fq7EEVRdDgcoslkEgGIer1eLCoqCnHi6vw5B4fDIer1etFsNot6vV42w4NE0b/zyM/PF00mk2g2m0Wz2SyL88jPzxcNBoMIQDoPl0C+rmn2IEIIqUVUXHoTQkh9UKEkhJBaUKEkhJBaUKEkhJBaUKEkhJBaUKEkhJBaUKEkhJBaUKEkhJBaUKEkhJBaUKEkhJBaRPV8lCS6uGbmttvtSElJAc/zKCwslM2CZUS+qEVJoobNZoNer8eQIUOQlJQEnU4Hq9Uqi9nribxRi5JEDdckwDzPIzk5GQBgt9tZRiJhglqUJGq4Lq9zc3Ol9V7CZeJZwhYVShIVsrOzYTQapclcXRO55uXlMU5GwgHNR0migs1mgyAIUCqVUCgU0szX4bJwGWGLCiUhhNSCLr0JIaQWVCgJIaQWVCgJIaQWVCgJIaQWVCgJIaQWVCgJIaQWVCgJIaQW/w84MbRzGoJedQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 350x262.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scienceplots # 导入'science'画图模块\n",
    "plt.style.use('science') # 采用'science'画图模块\n",
    "fig, ax = plt.subplots() # 建立画布\n",
    "x = np.linspace(0,1,100) # x轴点数\n",
    "c0 = -4.40\n",
    "c1 = -4.99\n",
    "c2 = 4.99\n",
    "y1 = x*(x-1)*(c0+c1*x+c2*x**2) # 近似解\n",
    "y2 = np.sqrt(2) *np.sin(np.pi* x) # 精确解\n",
    "ax.plot(x,y1,linewidth = '0.7',label=r'Approximate solution',color = 'k',linestyle='--') \n",
    "ax.plot(x,y2,linewidth = '0.7',label=r'Exact solution',color = 'k') \n",
    "ax.set_xlabel('$x$') # 设置横坐标名称\n",
    "ax.set_ylabel('$y(x)$') # 设置总坐标名称\n",
    "ax.spines['right'].set_visible(False) # 不显示右边框\n",
    "ax.spines['top'].set_visible(False) # 不显示上边框\n",
    "ax.legend() # 显示标签\n",
    "visible_ticks = { # 设定参数以不显示上和右刻度\n",
    "   \"top\": False,\n",
    "   \"right\": False\n",
    "}\n",
    "ax.tick_params(axis=\"both\", which=\"both\", **visible_ticks) # 去处上和右刻度\n",
    "fig.savefig('Ritz_fig３.png',dpi=600) # 保存图片\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f9d9d9f-8adc-4799-a59a-427b20978ab6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
